Rinse the tuna steaks and pat dry with paper towel. Grate the zest from the lime then squeeze the juice and set aside.

In a small bowl, combine lime zest, thyme, pepper and salt; stir to mix. Lightly rub both sides of the tuna steak with the EVOO. Rub the seasoning mix on the tuna steaks; coating them well.

Using a heavy bottomed saute pan, warm the EVOO. Increase the heat to high and place the tuna in the pan. Sear for 1 minute, then turn over carefully, reducing the heat to medium. Sear the other side for 1 more minute until medium rare. ( DO NOT OVERCOOK THE TUNA OF THE MEAT WILL BECOME DRY AND LOSE ITS FLAVOR.) Pour the lime juice over the tuna steaks right after you take them from the stove, then Serve.